Algebraic numbers, lattices and applications

• Grant number: 22/12667-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Robson Ricardo de Araujo
• Grantee: Cleber Luiz de Oliveira Santos
• Host Institution: Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP). Campus Cubatão. Cubatão , SP, Brazil

Abstract

This research project consists of an introductory study on algebraic number theory, its articulations with lattice theory and an overview of some of its theoretical and practical applications. The topics covered involve studies on algebraic numbers, number fields, rings of integers, quadratic and cyclotomic fields, ramification of ideals, lattices, Minkowski embedding, elliptic curves, among others.